Gibbs processes form an important class of point processes.
In (mathematical) physics they describe the thermodynamical behavior
of interacting particles; see [1]}. As a mathematical model they are much more
versatile than the completely independent Poisson process
(see e.g. [2]}). They are also quite popular
in spatial statistics; see e.g. [3]}, [4]}.
Getting a handle on distributional properties of Gibbs processes is not easy.
However, starting with the seminal paper [5]}, the last decade
has seen some efforts to understand some asymptotic
properties of functionals of Gibbs processes in infinite volume, at least
if the process is in a certain sense
close to a Poisson process. Our paper aims at adding
to this development.
